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8-1-2014
Measurements of Turbulent Mixing and Subsiding
Shells in Trade Wind Cumuli
Jeannine Katzwinkel
Leibniz Institute for Tropospheric Research, [email protected]
Holger Siebert
Leibniz Institute for Tropospheric Research
Thijs Heus
Cleveland State University, [email protected]
Raymond A. Shaw
Michigan Technological University
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Repository Citation
Katzwinkel, Jeannine; Siebert, Holger; Heus, Thijs; and Shaw, Raymond A., "Measurements of Turbulent Mixing and Subsiding Shells
in Trade Wind Cumuli" (2014). Physics Faculty Publications. 221.
http://engagedscholarship.csuohio.edu/sciphysics_facpub/221
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JOURNAL OF THE ATMOSPHERIC SCIENCES
VOLUME 71
Measurements of Turbulent Mixing and Subsiding Shells in Trade Wind Cumuli
JEANNINE KATZWINKEL AND HOLGER SIEBERT
Leibniz Institute for Tropospheric Research, Leipzig, Germany
THIJS HEUS
University of Cologne, Cologne, Germany
RAYMOND A. SHAW
Department of Physics, Michigan Technological University, Houghton, Michigan
(Manuscript received 22 July 2013, in final form 21 March 2014)
ABSTRACT
High-resolution measurements of the turbulent, thermodynamic, and microphysical structure of the edges
of trade wind cumuli have been performed with the Airborne Cloud Turbulence Observation System. Lateral
entrainment of subsaturated air into the cloud region leads to an evaporative cooling effect. The negatively
buoyant air partly enhances the compensating downdraft, forming a subsiding shell at cloud edge. Based on
the presented observations, the subsiding shell is divided into a turbulent and humid inner shell adjacent to the
cloud interior and a nonbuoyant, nonturbulent outer shell. In the trade wind region, continuous development
of shallow cumuli over the day allows for an analysis of the properties of both shells as a function of different
cloud evolution stages. The shallow cumuli are divided into actively growing, decelerated, and dissolving
based on cloud properties. As the cumuli evolve from actively growing to dissolving, the subsaturated
environmental air is mixed deeper and deeper into the cloud region and the subsiding shell grows at the
expense of the cloud. This measured evolution of the subsiding shell compares favorably with the predictions
of a direct numerical simulation of an idealized subsiding shell. The thickness of the measured outer shell
decreases with the evolution of the cumuli while the intensity of the downdraft is nearly constant.
1. Introduction
Cumulus clouds cover large areas of the Earth and
play an important role in its energy budget, but their
complex dynamical structure is not fully understood.
The cloud evolution and its lifetime are influenced by
dynamical processes over the full range of the turbulent
energy cascade and their interplay among each other.
One major issue in this context is the entrainment process at cloud edge whose analysis started with the works
of Stommel (1947) and Squires and Warner (1957).
Entrainment defines the transport of environmental air
into the cloud region either from the side (lateral entrainment) or from above the cloud (cloud-top entrainment). The subsequent mixing between environmental
Corresponding author address: Jeannine Katzwinkel, Leibniz
Institute for Tropospheric Research, Permoserstraße 15, 04318
Leipzig, Germany.
E-mail: [email protected]
DOI: 10.1175/JAS-D-13-0222.1
Ó 2014 American Meteorological Society
and cloudy air leads to reduction of liquid water content through dilution and the evaporation of cloud
droplets, and the resulting latent heating alters the
buoyancy field surrounding and inside the cloud. Although the spatial resolution of both model simulation
and experiments has improved during the last several
decades, there are still open questions about the entrainment process and how it influences cloud microphysics and cloud dynamics.
Here we focus on the small-scale turbulent structure
at the edge of cumuli where lateral entrainment and the
subsequent mixing between subsaturated environmental and cloudy air leads to the development of a thin
‘‘subsiding shell.’’ A first indication of this shell was given
by a laboratory experiment performed by Woodward
(1959), which indicated a cumulus cloud as a thermal
characterized by a body of updrafts surrounded by
a shell of downdrafts. This picture was further clarified
by aircraft and radar studies of small, maritime cumuli by
Jonas (1990) and Knight and Miller (1998). Jonas (1990)
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KATZWINKEL ET AL.
further pointed out that the presence of the subsiding
shell increases the entrainment instability at cloud edge
by transporting cloud-top air to lower levels. Tracer experiments performed by Stith (1992) confirm such transport and showed the lateral entrainment of these tracer
parcels at lower levels.
The first assumption of Jonas (1990) referred to
a mechanical forcing driving the downdrafts, but this
was refuted by aircraft observations performed by Rodts
et al. (2003). They observed a conspicuous dip in the
virtual potential temperature profile and no dip in the
total water mixing ratio profile at cloud edge, providing
evidence for evaporative cooling as the driving mechanism of the subsiding shell. These observations were
compared with a large-eddy simulation (LES) by Heus
and Jonker (2008) and the numerical calculation of the
individual terms of the vertical momentum equation
confirmed the assumption that buoyancy is the dominant force in the subsiding shell. Heus and Jonker (2008)
discussed further that the transport of cloud-top air
down to lower levels within the subsiding shell refreshes
the air at cloud edge, which influences the lateral mixing
process and could create a stronger subsiding shell. The
same effect can also be generated by an increase in aerosol
concentration, which seems to enhance the evaporative
cooling rate at cloud edge, leading to enhanced negatively buoyant air at cloud edge (Small et al. 2009). The
important role of the subsiding shell for cloud dynamics
is further indicated by the increased turbulence intensity
within the shell (Siebert et al. 2006b) and the different
air properties between subsiding shell and far environment in terms of humidity and buoyancy (Jonker et al.
2008). The entrainment of this preconditioned air instead of subsaturated far-environmental air influences
the microphysical response to mixing (Gerber et al.
2008).
A detailed analysis of the shell properties, however,
has been challenging because the horizontal extent of
a typical shell is comparable to or less than the resolution of LES cloud models or of aircraft data. Two detailed studies of the structure of cumulus clouds are given
by Wang et al. (2009) and Wang and Geerts (2010). The
first study analyzed the dynamics of the cloud margin
with a thickness of 10% of the cloud diameter, which is
characterized by sinking and relatively cold air. The
second study characterized negative buoyancy, cold temperature anomalies, and downward motion as typical
properties of air in the vicinity of the cloud edge. Nevertheless, they were not able to resolve the small-scale
fluctuations due to a spatial resolution of 10 and 5 m,
respectively. Also, LESs do not resolve the smallest
scales leading mostly to an underestimation of the amplitude of the downdrafts within the subsiding shell by
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LESs compared to observations (Heus et al. 2009).
Abma et al. (2013) addressed these LES limitations by
performing the first fully resolved computational study
of the finescale structure of turbulent mixing and the
formation of a subsiding shell. The time evolution of
a small portion of an idealized subsiding shell was analyzed based on direct numerical simulations (DNS). The
results show that during the lateral entrainment and
mixing process, the thickness of the subsiding shell
grows quadratically and the downdrafts increase linearly
with time. Coupling to large scales remains an open aspect of this problem, however.
The current paper presents the first high-resolution
measurements of the finescale structure of subsiding
shells in cumulus clouds. The measurements were performed with the slow-moving helicopterborne measurement payload Airborne Cloud Turbulence Observation
System (ACTOS), which allows for simultaneous and
collocated characterization of cloud microphysical, thermodynamic, and turbulence properties at centimeter and
decimeter scales. The subsiding shells were measured at
the edge of trade wind cumuli. These clouds were selected for this study because the trade wind region is
often populated, at any given time, by cumulus convection at all stages of development, which provides the
opportunity to analyze the evolution of the subsiding
shell. The measurements provide insight into the detailed structure of the subsiding shell and how it varies
during the growth and decay stages of cumulus convection. This picture then allows us to make a first effort
toward comparing measurements with the idealized
DNS results of Abma et al. (2013).
The paper is organized as follows: Section 2 describes
the measurement platform ACTOS and its instrumentation. Section 3 describes the basic methods for the data
analysis. In section 4 the characteristics of the trade wind
cumuli are presented, while section 5 deals with the characteristics of the cloud edge. The comparison of the measurements with DNS is presented in section 6. The paper
concludes with a summary and discussion.
2. Experimental
High-resolution measurements in trade wind cumuli
over the ocean near the eastern coast of Barbados were
made during the Clouds, Aerosol, Radiation and Turbulence in the Trade Wind Regime over Barbados
(CARRIBA) campaign in November 2010 and April 2011
(Siebert et al. 2013). The measurements were performed
with the helicopterborne measurement payload ACTOS, whose main details are summarized here. ACTOS
is located below a helicopter on a 140-m-long rope and
operates with a true airspeed of 20 m s21. Assuming
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a given sampling frequency of 100 Hz, a spatial resolution down to decimeter scale is realized. The turbulence
measurements were performed with a hot wire anemometer with a sampling frequency of 2 kHz. The influence of droplet impactions on the thin wire under
cloudy conditions was considered by applying a despiking algorithm described in Siebert et al. (2007). After
despiking, the final resolution is 438 Hz. Besides the
turbulence measurements, the following measurements
are used for the analysis in this paper: temperature
T measured with a special cloud thermometer [ultrafast
thermometer (UFT); Haman et al. 1997], absolute humidity a measured with a dewpoint hygrometer (TP 3-S,
MeteoLabor, Switzerland) and an open infrared absorption hygrometer (LiCor 7500, LI-COR corporation,
United States), pressure p measured with a Barocap
Vaisala sensor (Vaisala, Finland), liquid water content
(LWC) measured with a particle volume monitor (PVM100A; Gerber et al. 1994), and the three-dimensional wind
vector measured with an ultrasonic anemometer Solent
HS (Gill Instruments, United Kingdom). The sonic
measurements are corrected for attitude and platform
velocity. For more information concerning ACTOS the
reader is referred to Siebert et al. (2006a). All deployed
devices have sufficient resolution for our kind of analysis: the ultrasonic anemometer resolves the wind vector components in centimeters per second (Siebert and
Muschinski 2001). The temperature obtained with the
UFT shows a resolution of better than 10 mK and the
standard deviation due to uncorrelated noise of the PVM100A is about 1 mg m23 [see Siebert et al. (2003) for
a detailed determination of the noise floor for PVM100A and UFT]. All devices have a temporal resolution of at least 100 Hz; therefore, we can safely conclude that our results are not significantly affected by
spatial or temporal resolution. All data were collected
by performing nearly horizontal flight legs through
shallow cumulus clouds approximately 100 m below
cloud top owing to the visual flight restrictions of the
helicopter.
3. Methods
In this section we outline the basic methods for the
analysis of the high-resolution measurements within
a large number of trade wind cumuli. All measurements
used herein have a spatial resolution of 0.2 m except the
local energy dissipation rate, which is explained later.
We identify quantitative criteria for defining the cloud
and the subsiding-shell regions within the selected
clouds. The selection is based on certain conditions that
allow for a statistical analysis. Furthermore, because
the trade wind environment allows clouds to be
VOLUME 71
FIG. 1. Illustration of the different cloud and subsiding-shell
regions and their characteristics.
sampled at all stages of development, the statistical
analysis suggests a natural definition of three evolutionary stages: actively growing, decelerating, and dissolving
clouds.
The criteria for the cloud and subsiding shell regions
specified here are determined in the context of 1) an
effort to be generally consistent with the definitions
given in the recent literature on subsiding shells and 2)
the fact that ACTOS data are taken at very high resolution and therefore reveal levels of detail in fluctuating
quantities that need to be considered in the definitions.
The cloud extent is fundamentally ambiguous because
of the lack of a clearly defined edge when viewed at high
resolution. In past studies (e.g., Rodts et al. 2003)
a threshold cloud droplet number density was chosen;
here we also use a threshold, but because number density is more difficult to estimate over very short flight
lengths, we use liquid water content. The region with
LWC . 0.2 g m23 is taken to define the cloud. The length
of this region is defined as the cloud diameter. It should
be noted that all measurements presented here were
taken within about 100 m of cloud top, so this threshold
is relatively conservative. Each flight transect through
a cloud is divided into three regions: environment,
subsiding shell, and cloud interior. Based on careful
observation of the data, and also consistent with the
work of Heus and Jonker (2008), the subsiding-shell
region is further divided into two regions: one negatively
buoyant as a result of cloud mixing and evaporation
(called the inner shell) and the other possessing nearly
the same buoyancy as the environment but with negative
velocity (called the outer shell). The characteristics of
these regions are discussed in detail later, but we provide
the defining criteria here. A schematic picture of the different regions including the characteristics of the boundaries is shown in Fig. 1.
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KATZWINKEL ET AL.
The inner shell is characterized by being adjacent to
the cloud interior and by being negatively buoyant. It is
therefore defined by the following two boundaries: the
outside boundary is located where buoyancy B begins to
decrease below zero (denoted XjB0 ), and the inside
boundary is located where w changes from downdraft to
updraft or where B changes from negative to positive
within or at the edge of the region with LWC . 0.2 g m23
(denoted Xjw0 ).
The outer shell is characterized by not being negatively buoyant like the inner shell, but still showing
negative velocities. It is therefore defined by the following two boundaries: the outside boundary is located
where w starts to decrease below the environmental
value of nearly zero, and the inside boundary is located
where B starts to decrease below zero (i.e., the outer
boundary of the inner shell).
It should be noted that these criteria allow that the
negatively buoyant region of the subsiding shell can
encompass a portion of the cloud (i.e., regions with
LWC . 0.2 g m23). As opposed to the inner shell, the
cloud interior is the part of the cloud that is not directly
affected by entrainment of environmental air. The
boundary between the inner shell and the cloud interior
is denoted with the above mentioned parameter Xjw0 .
For the purpose of a statistical analysis of the cloud
and subsiding shell regions, we define the following
conditions for selecting individual clouds. First, small
cloud fragments are excluded from the analysis. This
means that the diameter of the cloud and LWC in the
cloud region have to be larger than 50 m and 0.2 g m23,
respectively. Second, two neighboring clouds have to be
sufficiently well separated from each other so as to define a clear, cloud-free environment between subsequent
clouds. Therefore, the distance to the next cloud has to
be larger than 100 m. This comparable short distance
between two neighboring clouds is critical but a good
compromise to get enough clouds for our analysis without
observing an interference between to subsequent subsiding shells. With these conditions, 217 clouds are
selected.
Typically, in the trade wind region clouds at different
stages of evolution can be found close to each other.
Frequently, actively growing clouds are observed adjacent to dissolving ones. This is caused by the continuous
development of shallow cumuli under quite homogeneous conditions in terms of sea surface temperature
and mesoscale dynamics. The observations suggest that
the cloud evolution can be divided into three stages of
development. Each stage is defined based on the 90th
percentile values for updraft velocity and buoyancy,
w90% and B90% respectively, as observed within the
cloud (i.e., the region with LWC . 0.2 g m23):
d
d
d
active, for w90% . 0 and B90% . 0;
decelerated, for w90% . 0 and B90% , 0; and
dissolving, for w90% , 0 and B90% , 0.
Further details of the analysis, specific examples, and
averaged observations are given later.
The characterization of the subsiding shell regions
and the three stages of development is based on
buoyancy. Here, we calculate this parameter as B 5
g(Qy 2 Qy )/(Qy ), where Qy is the virtual potential
temperature calculated as Qy 5 Q(1 1 0.61qt 2 1.61ql),
where qt and ql denote the total water and liquid water
mixing ratios. The overbar denotes the cloud-free
environmental mean value calculated for each cloud
individually.
The further analysis of the high-resolution measurements is based on the calculation of a local energy dissipation rate «t where we applied two different methods.
In the first method, the basic definition of «t is used with
the assumption of the validity of the Taylor hypothesis
and local isotropy (Wyngaard 2010):
«t [
15n
(› u)2 ,
U TAS t t
(1)
where n denotes the kinematic viscosity, UTAS and ›tu
denote the true airspeed and the temporal derivative of
the longitudinal wind velocity component measured
with the hot wire anemometer, and ()t denotes the
average of the respective parameter over the integration
time t. Here, we apply a moving window with a width of
100 samples to the despiked hot wire data with 438-Hz
resolution, which yields a spatial resolution of l 5
UTAS /f ’ 5 cm. This method is conducive to calculating
the spatial structure of the «t —especially at cloud edge
where high variability exists. The absolute values are
underestimated because for an accurate estimate of «t ,
a spatial resolution on the order of 10h ’ 1 cm is necessary, where h ’ 1 mm is the Kolmogorov length scale.
In the second method, which allows a more precise value
of «t to be determined with coarse-grained data, the
dissipation rate is estimated from the second-order
structure function S(2)(t 0 ):
«t ’
f0:5[S(2) (t0 )]t g3/2
(t0 U TAS )
,
(2)
where S(2)(t0 ) 5 [u(t 1 t0 ) 2 u(t)]2. Here, S(2) is estimated
for nonoverlapping subrecords of the longitudinal velocity component measured with the ultrasonic anemometer; therefore, no correction for the presence of
cloud droplets is necessary. The chosen subrecord length
of 100 samples yields a spatial resolution for «t of 20 m.
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FIG. 2. A single cloud penetration: (a) LWC, (b) temperature and absolute humidity (the red
line denotes measurements with the infrared-absorption hygrometer LiCor and the dot–dashed
red line marks measurements performed with the dewpoint hygrometer), (c) vertical wind
velocity, (d) buoyancy, (e) energy dissipation rate [the black line denotes the direct method and
the crosses mark the absolute values calculated based on S(2)(t0 )], and (f) liquid water potential
temperature and mixing fraction. The white region between the two gray regions marks
the cloud interior and the two gray regions denote the subsiding shell at the edges of the cloud.
The vertical black dashed line divides the subsiding shell into the inner shell (denoted I) and the
outer shell (denoted II).
A detailed description of both methods is given in Siebert
et al. (2006b).
4. Statistical cloud analysis
This section deals with the observed thermodynamic
and microphysical properties as well as the turbulent
and mean velocity profiles that were used to characterize the cloud interior and the subsiding shell and cloudfree environment regions. In Fig. 2, we illustrate the
different cloud regions with a specific example taken
from a single cloud penetration on 24 November 2010.
For this specific example, the cloud region with LWC .
0.2 g m23 is not directly affected by entrainment of environmental air and so this whole region is equated to
the cloud interior. The cloud region is characterized by
nearly constant values of a 5 17 g m23 and T 5 218C, w .
0 with peak values of up to 2.5 m s21, B . 0 with an average of about 0.01 m s22, and «t ; 1023 m2 s23 . Hence,
this example represents an actively growing cloud. The
liquid water potential temperature Ql 5 Q 2 (qlLyQ)/
(cpT), where Ly is the latent heat of vaporization and cp is
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KATZWINKEL ET AL.
the specific heat at constant air pressure (Betts 1973),
shows a mean value of 289 K. In the cloud-free environment, «t and a decrease to 1024 m2 s23 and 14.5 g m23,
respectively, T shows similar values as inside the cloud
interior, w and B fluctuate around zero, and Ql 5 302 K.
The subsiding shell at cloud edge is marked in Fig. 2 by
the gray regions located between the cloud-free environment and the cloud interior, adjacent to both sides.
For this specific example, these regions are characterized by a residual LWC , 0.1 g m23 with a high variability, illustrating the eddylike structure of the cloud
edge. A closer look shows that inside this subsiding shell
region, «t increases from environmental values to values
even higher than in the cloud interior (black line in Fig.
2e). At the same point, B starts to decrease. Based on
these observations, the subsiding-shell region is further
divided into two shells (indicated by the vertical dashed
black lines). The inner shell (denoted with ‘‘I’’), adjacent to the cloud interior, is characterized by reduced
values of T, w , 0, B , 0, and «t ; 1022 m2 s23 , again
higher compared with the cloud interior. Additionally,
a increases from environmental values to nearly cloud
values within this region. It should be noted, however,
that the humidity measurements do not allow a detailed
look at the fluctuations because of the significantly reduced spatial resolution. The dewpoint hygrometer
(dotted red line) measures only with a spatial resolution
of 20 m and the LiCor (straight red line) was used as
a closed system to reduce the cloud droplet impaction.
To analyze the humidity fluctuations in the inner shell,
highly resolved measurements such as with a Lymanalpha absorption hygrometer would be necessary. The
turbulent and humid inner shell was analyzed with LESs
by Heus and Jonker (2008). Between the inner shell and
the cloud-free environment the outer shell is observed,
here denoted with ‘‘II.’’ This region is characterized by
temperature and humidity comparable to the environmental values, a slight downdraft with B ’ 0, and a
comparably small «t .
The origin of the air within the inner and outer shell
can be investigated by using the liquid water potential
temperature and the total water content, both of which
are conserved variables during mixing. The outer shell
consists mostly of environmental air, which can be seen
in Fig. 2f by the values of Ql and mixing fraction x (Kain
and Fritsch 1990) that are similar to the environment
values. Here, x 5 (qt 2 qtc )/(qte 2 qtc ), where the subscripts c and e denote the cloud and environmental
values, respectively, and the overbar denotes the average value in the corresponding regime. In contrast, the
air inside the inner shell is a mixture of environmental
and cloud air as indicated by the mean value of Ql 5
299 K within this inner shell. Also, x shows a nearly
2815
FIG. 3. The variability of all 217 selected clouds is represented by
the PDFs of the 90th percentiles of (a) normalized liquid water
content, (b) buoyancy, and (c) vertical wind velocity inside the
cloud.
linear decrease with same variability toward the cloud
interior with a minimum value of 0.7 indicating a mixture of 70% environmental and 30% cloudy air. Although, it has been previously assumed that lateral
mixing is the leading mechanism for the development of
the inner shell (Heus and Jonker 2008), no definite
statement about the mixing process can be made based
on the data presented here. Evidence for this assumption could be the calculated mixing temperature of
Qlm 5 xQle 1 (1 2 x)Qlc 5 299:6 K, which is nearly the
same as the observed mean value within the shell. But
the mean value of Ql could also be interpreted as being
a result of mixing of cloud air with clear air from above
indicated by an estimated lapse rate of 0.5 K (100 m)21
for Ql under cloud-free conditions. In either case, the
turbulent mixing of these two air masses leads to an
evaporative cooling effect resulting in negatively buoyant air at cloud edge.
The statistics of the parameters B90% and w90% which
are used to define the different cloud life stages together
with the 90th percentile of the normalized LWC (normalized with the calculated adiabatic value) (LWCnorm 90%) is
analyzed. In Fig. 3a, the distribution of LWCnorm 90% varies
in a broad range between 0.1 and 0.8 times the adiabaticcalculated value. The probability density function (PDF)
of B90% shows positive values, indicating actively growing
clouds, and also negative values inside the cloud (Fig. 3b).
Figure 3c shows the PDF of w90% representing a majority
of clouds with an updraft inside the cloud. But a few
clouds with downdrafts inside the cloud are measured,
indicating dissolving clouds.
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VOLUME 71
the fact that the inner shell covers the whole cloud in this
stage of evolution. Hence, in the dissolving case no cloud
interior is identified and, therefore, the high values of
LWC and «t are found in the inner shell. In the cloud
interior, the actively growing and decelerated clouds
show only small differences concerning LWC, w, and «t .
The mean buoyancy shows positive values for the actively growing clouds and negative values in the decelerated case, which is in agreement with the definition
in section 3.
5. Characterization of the cloud edge
FIG. 4. Rescaled averaged cross sections for (from top to bottom)
liquid water content, vertical wind velocity, buoyancy, and energy
dissipation rate within the cloud interior and subsiding shellregions. The black curve denotes the actively growing clouds, the
red line denotes the decelerated clouds, and the blue line denotes
the dissolving clouds. For each cloud individually, the different
regions are scaled with their one typical dimension and averaged
afterward.
For all three stages of development (actively growing,
decelerated, and dissolving), we calculated rescaled averaged cross sections for LWC, w, B, and «t within the
cloud and subsiding shell regions. The results are shown
in Fig. 4, in which the black line represents the average
of actively growing clouds, the red line represents the
average of the decelerated ones, and the blue line denotes the average of the dissolving clouds. The individual
regions are rescaled with their own typical dimension for
each cloud individually and are averaged afterward. For
all stages, the cloud-free environment is characterized
by zero liquid water content, values of w and B around
zero, and a small «t on the order of 1024 m2 s23. Beside
the value of B around zero for all stages, increased
variability is obvious within the outer shell. Especially
the dissolving clouds differ from the actively growing
and decelerated clouds. The dissolving clouds show
nearly no LWC and a higher «t within the outer shell.
Additionally, the nearly linear decrease of w obvious for
all stages is intensified for the dissolving clouds. The
characterization of the inner shell with w , 0 and B ,
0 is obvious for all stages of development. The high
variability for the dissolving clouds can be explained by
In the following, the analysis of the edges—in particular the subsiding shells (see Fig. 2)—of 217 shallow
cumulus clouds is presented. Only edges sampled while
entering the cloud have been considered to minimize
any possible influence of wetting of the temperature
probe.
The characterization of the inner shell is based on
three main parameters. One parameter is the thickness
of this shell whose calculation based on the definition by
Abma et al. (2013):
d5
1
B10%
ðXj
w0
X jB
B dx,
(3)
0
where XjB0 and Xjw0 denote the two boundaries of the
inner shell. Here, the integral is normalized with the 10th
percentile of the buoyancy calculated within the integration limits. The use of the 10th percentile instead of
the minimum values as described by Abma et al. (2013)
is simply a result of the dependency of the measured
minimum value on the measurement resolution. The
second and third parameters for characterizing the inner
shell are the 10th percentile of buoyancy and the 10th
percentile of the vertical wind velocity w10% calculated
also within the integration limits.
Figure 5 shows examples of cloud edges for each of the
cloud evolution stages—the criteria for which were defined in section 3. These clouds were measured on 14
November 2010 and 14 and 16 April 2011. The x axis
shows the distance relative to the entrance of the cloud
(CE). For all cases, 200 m in front of the cloud and 100 m
of the cloud itself are shown. The different regions are
marked with vertical black lines and a corresponding
identifier (e.g., ‘‘env’’ as environment). The thickness of
the inner shell clearly differs in Fig. 5 depending on the
stages of evolution. In the case of the actively growing
cloud, d is about 7 m with w10% 5 21.7 m s21 and B10% 5
20.008 m s22. Additionally, the outer shell is apparent
with a thickness of 60 m. The decelerated cloud shows
a distinct inner shell with a broader thickness of about
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KATZWINKEL ET AL.
FIG. 5. Examples of cloud edges for each of the three stages of
evolution of the trade wind cumuli: (a) actively growing cloud with
w90% . 0 and B90% . 0, (b) decelerated cloud with w90% . 0 and
B90% , 0, and (c) dissolving cloud with w90% , 0 and B90% , 0. The
color code is the same in all panels: blue regions mark the liquid
water content, black lines denote the vertical wind velocity, and
green and red lines mark the energy dissipation rate and the
buoyancy, respectively. The entrance of the cloud interior is denoted by x 5 0 m, indicated by LWC . 0.2 g m23.
20 m and a downdraft of w10% 5 21.5 m s21 and B10% 5
20.01 m s22. Additionally, a smaller thickness of 45 m is
observed for the outer shell. In the case of the dissolving
cloud an intense downdraft inside the inner subsiding
shell of w10% 5 23.8 m s21 and B10% 5 20.06 m s22 is
observed. The thickness of this shell increases to nearly
170 m, and no outer shell is observed.
Figure 6 shows the PDFs of the characteristic parameters (w10%, B10%, and d) of the inner shells. The
measured 10th percentile of downdraft inside the inner
shells varies between 0 and 25 m s21 (Fig. 6a). Figure 6b
shows the PDF of B10%, where most of the values lie in
the range from 0 to 20.02 m s22. Additionally, clouds
with a positive buoyancy are observed and also a few
clouds show a very strong negative buoyancy as low as
20.08 m s22. The PDF of d is shown in Fig. 6c, where the
y axis is logarithmic for better clarity. The values vary
from below 1 to 175 m with only a few values observed
with d . 80 m.
Table 1 summarizes the median properties of the
cloud and subsiding-shell regions as a function of the
evolution stages. All parameters were first calculated for
individual clouds and afterward averaged giving one
median value for each evolution stage. The number of
clouds grouped in the different evolution stages is given
by n. The majority of the observed clouds were actively
growing; thus, only a few dissolving clouds are considered. This is a result of the stringent criteria for cloud
2817
FIG. 6. PDF of (a) minimum downdraft velocity, (b) minimum
buoyancy inside the inner shell, and (c) the thickness of the inner
shell.
selection. Most of the dissolving clouds are rejected
because of their low values of LWC or the narrow cloud
diameter. With the evolution from an actively growing
cloud to a dissolving one, w90% decreases from 2.2 m s21
updraft to a downdraft of 20.8 m s21, while within the
inner shell, an increase in the absolute values of w10%
and B10% is observed. Furthermore, Xjw0 shifts more and
more into the cloud region, which is indicated by an increasing distance between CE and Xjw0 [D(Xjw0 2 CE)].
The mixing process and evaporation of cloud droplets
therefore leads to an increasing thickness of the inner
shell d, while the cloud diameter decreases. A nearly
constant distance between XjB0 of the inner shell and
the middle of the cloud region (CM) at around 90 m
[D(CM 2 XjB0 )] supports the results of Abma et al.
(2013) that the inner shell expands primarily into the
cloud region. The outer shell is observed at the edge of
actively growing clouds with a relative frequency of
82%, but also half of the dissolving clouds are surrounded by such a shell. With the evolution from an
actively growing cloud to a dissolving one, the median
thickness of the outer shell dd decreases, while the
downdraft inside this shell fluctuates around wd ;
20.3 m s21 for all stages of evolution.
6. Comparison with model results
In this section, we explore the consistency of our statistical results with the direct numerical simulations by
Abma et al. (2013). A brief description of the model is
given here; for further details, the reader is referred to
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JOURNAL OF THE ATMOSPHERIC SCIENCES
VOLUME 71
TABLE 1. Median properties of all selected clouds for each stage of evolution. These properties are the 90th percentile of w inside the cloud
w90%, 10th percentile of the downdraft velocity w10% and the buoyancy B10% inside the inner shell, distance between the boundary of the
inner shell close to the cloud region Xjw0 and CE [D(Xjw0 2 CE)], the thickness of the inner shell d, cloud diameter (cd), distance between
the cloud-free boundary of the inner shell XjB0 and the middle of the cloud (CM) [D(CM 2 XjB0 )], the relative frequency of the outer shell
f, median thickness of the outer shell dd, and median downdraft velocity wd inside the outer shell.
n
w90% (m s21)
w10% (m s21)
B10% (m s22)
D(Xjw0 2 CE) (m)
d (m)
cd (m)
D(CM 2 XjB0 ) (m)
f (%)
dd (m)
wd (m s21)
Actively growing
(w90% . 0, B90% . 0)
Decelerated
(w90% . 0, B90% , 0)
Dissolving
(w90% , 0, B90% , 0)
122
2.2
20.3
20.002
6
2
178
99
82
68
20.32
79
1.6
21.0
20.016
12
16
120
82
70
47
20.25
14
20.8
21.9
20.033
76
82
82
96
45
6
20.45
Abma et al. (2013). DNS fully resolves turbulence down
to dissipation scales, sacrificing instead the large-eddy
structure through an idealized setup. Furthermore, approximations are made in the treatment of cloud microphysics. To simulate the lateral entrainment process
at the side of a single shallow cumulus, the model is
based on a two-layer system including an environmental
and a cloud region that are well separated. Both regions
are characterized by zero vertical wind velocity and zero
buoyancy. Therefore, in contrast to our measurements,
no compensation flow exists at cloud edge. A broadband
perturbation initiates the mixing between the subsaturated
environmental air and the cloudy air. The subsequent
evaporation of droplets leads to a cooling effect, resulting in negatively buoyant air at cloud edge. This
initiates the development of the buoyant subsiding shell.
With increasing time, the simulated subsiding shell grows
owing to further turbulent mixing between the environmental and cloudy air. The DNS results basically show
a quadratic growth in the thickness of the subsiding shell
and a linear increase of the downdraft velocity with time.
Based on self-similarity arguments, these findings can be
described by the following equations (Abma et al. 2013):
B
dm (t) 5 c1 c2 m (t 2 tm1 )2
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2c1 c2 Bm dm1 (t 2 tm1 ) 1 dm1 ,
(4)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c
wm 5 2 1 Bm dm .
c2
(5)
Here, dm is the thickness of the simulated subsiding shell
and Bm and wm denote the minimum values of buoyancy
and vertical wind velocity within the simulated subsiding
shell. According to the simulation of Abma et al. (2013),
the initial condition tm1 and dm1 are set to 5 s and
0.054 m, respectively, and the constants c1 and c2 are
determined to be 0.24 and 0.1.
The basis for the comparison of measurements and
the simulation is given by the main properties of the
inner shell: d, w10%, and B10% for measurements and dm,
wm, and Bm for the simulated subsiding shell. While the
measurements are performed at the edges of numerous
clouds in different stages of evolution, the simulation
considers one single cloud edge and the evolution of the
corresponding subsiding shell. This evolution is calculated every 10 s according to Eqs. (4) and (5), and it was
observed that the value of Bm increases linearly until
reaching a typical value of 0.02 m s22 during the first 30 s
and remains constant afterward. Consistent with the
latter stages of the simulation, Bm is taken as a constant
for the subsequent comparison with data.
Figure 7 shows the correlation between downdraft
intensity and thickness of the buoyant subsiding shell in
Fig. 7a and between downdraft intensity and buoyancy
in Fig. 7b. All correlations are plotted for the simulated
subsiding shell (red lines) and for the measured values of
the inner shell (boxes). In Fig. 7a, the simulation shows
a quadratic dependence of dm on wm. The measured d
also increases with decreasing w10%, but the measurement uncertainty does not allow for definitive statement
about a linear, quadratic, or other relationship. The
decreasing number of measured values with increasing
downdraft intensity leads to an increasing statistical
uncertainty that makes rigorous conclusions difficult.
Nevertheless, the measurements are in the range of the
model prediction and a similar tendency and absolute
values are observed. A similar behavior is seen for the
correlations shown in Fig. 7b. After the first seconds, the
AUGUST 2014
KATZWINKEL ET AL.
FIG. 7. Comparison of the measured (d, w10%, B10%; boxes) and
simulated (dm, wm, Bm; red lines) properties of the inner shell:
(a) thickness of the inner shell vs the downdraft velocity in the inner
shell and (b) buoyancy vs the downdraft velocity in the inner shell.
simulated value Bm remains constant with increasing
downdraft intensity. The same tendency is evident in the
measurements despite their relatively large spread.
7. Summary and discussion
Helicopterborne observations with decimeter resolution were performed during the CARRIBA campaign
over Barbados. The observations provide a detailed insight into the edges of trade wind cumuli. The cloud
edges were characterized by highly increased turbulence
2819
compared to the cloud-free environment but also compared to the cloud region, which is an indication for
strong mixing. The key finding was a well-pronounced
subsiding shell that was observed in all of the 217 analyzed clouds. The width and the downdraft velocity of
these shells were found to depend on the evolution stage
of the clouds, which was defined by cloud parameters
such as buoyancy and updraft velocity. The findings are
illustrated in Fig. 8 for three typical cloud evolution
stages defined as an actively growing cloud defined by
positive buoyancy resulting in updrafts (B . 0 and w .
0) in the cloud (illustrated by the blue line) (Fig. 8a),
a decelerated cloud type with negative buoyancy (B , 0)
but still updrafts with reduced magnitude (w . 0) (Fig.
8b), and a dissolving cloud with negative buoyancy resulting in downdrafts (B , 0 and w , 0) (Fig. 8c). Because of flight restrictions, the helicopter had to remain
above the clouds; therefore, all measurements were
performed within 100 m of cloud top as illustrated by the
red horizontal line (see Fig. 8). The measured cloud
diameter (80–100 m) is probably smaller compared to
a typical cloud diameter as observed in the middle part
of a cloud, but it is expected that the general results can
be extended also to lower regions of the cloud.
The measured actively growing clouds (Fig. 8a) are
characterized by a comparably broad cloud region (cd)
with strong updrafts and are surrounded by a thin subsiding shell. The light gray region denotes the nonbuoyant, nonturbulent outer shell and the dark gray
region marks the turbulent and buoyant inner shell,
which has been developed because of the entrainment
and mixing process. Both regions are characterized by
FIG. 8. Schematic picture of the evolution of the cloud (blue line) and the subsiding shell regions as a function of the three stages of
evolution [(a) actively growing, (b) decelerated, and (c) dissolving]. The light gray region indicates the outer shell, the dark gray region
indicates the inner shell, and the white region within the cloud denotes the cloud interior. Here, d marks the distance from beginning of the
inner shell to the entrance of the cloud interior, the thickness of the cloud is marked with cd, and sb marks the thickness of the whole
system.
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JOURNAL OF THE ATMOSPHERIC SCIENCES
a weak downdraft while the outer shell is typically
broader than the thickness d of the inner shell. In this
case, only a small portion of the cloud is influenced by
entrainment of environmental air and so a broad cloud
interior (illustrated by the white region within the cloud)
is observed. With the evolution to decelerated clouds
(Fig. 8b), the subsaturated environmental air is mixed
deeper into the cloud and the inner shell grows at the
expense of the cloud interior. The width of the entire
cloud, including cloud and subsiding-shell regions, was
observed to remain nearly constant. Evaporative cooling due to lateral entrainment enhances the downdrafts
inside the inner shell, while the updrafts inside the cloud
region are decelerated because of negative buoyancy. In
contrast to the inner shell, the thickness of the outer
shell is reduced while the downdrafts in this region remain nearly constant. In the dissolving stage of the cloud
lifetime (Fig. 8c), the width and the downdraft velocity
of the inner shell increase further until the inner shell
covers the whole cloud. Hence, no cloud interior is observed and the whole cloud is influenced by the entrainment of environmental air, which may lead to the
complete dissolving of the cloud. Dissolving clouds show
a very small outer shell with a downdraft intensity that is
similar to the other two stages. The increasing thickness
of the inner shell with cloud evolution indicates an increasing entrainment of preconditioned air instead of
subsaturated far-environmental air influencing the microphysical cloud properties (Gerber et al. 2008).
The qualitative agreement of the observed correlations between downdraft intensity, width, and buoyancy
of the inner shell with results gained from DNS by Abma
et al. (2013) help corroborate the existence of a functional relationship between shell properties and cloud
evolution stage. The time evolution of dm in the DNS [cf.
Eq. (4)] allows an estimate of the evolution time of the
measured inner shell. For example, if we consider an
observed downdraft velocity of w10% 5 23.2 m s21 and
the corresponding inner-shell thickness of d 5 100 m (cf.
Fig. 7a), with the help of Eqs. (4) and (5), this data point
can be related to a model evolution time of t 5 670 s. But
one must keep in mind that this model evolution time
starts after the duration of the spinup phase and so does
not represent a real cloud age. Additionally, the model
ignores any large-scale cloud dynamics, making an interpretation of this time even more difficult. However,
this rough estimate provides some idea for future research as to how to estimate lifetime of an observed
cloud as a function of shell width.
Our observations of the subsiding shell are also in
good agreement with results derived from LES of an
unsaturated convective mixed region around a liquid
water cloud (Zhao and Austin 2005a,b). The dimensions
VOLUME 71
of their modeled trade wind cumuli are comparable to
our observations, which allows a direct comparison. The
unsaturated convective mixed region in the LES is first
smaller than the liquid water cloud and grows in thickness with the evolution of the cloud. It contains roughly
half of the liquid water cloud volume when the cloud top
reaches its maximum height. This is of the same magnitude as the relation between our measured cloud and
the subsiding shell thickness. The unsaturated convective mixed region reaches its maximum thickness shortly
before the liquid water cloud is completely evaporated.
In the case of an actively growing cloud, the airflow
inside the outer shell might be explained as a compensating flow owing to the strong updrafts inside the cloud
region. This picture is supported by the analysis of Heus
and Jonker (2008), who pointed out that 10% of the
upward mass flux in the cloud is compensated in the
region with B , 0 while another 13% is compensated by
being dragged along downward with the buoyant subsiding shell. A more detailed analysis of the massflux compensation by Jonker et al. (2008) leads to the
conclusion that ‘‘the compensating downward mass flux
takes place in the immediate proximity of clouds and not
in the form of a weak uniformly subsiding motion.’’
The whole subsiding shell, including the outer shell, is
also observed in the stage of dissolving clouds, so it
follows that there must be a mechanism that still results
in downward motion, although the upward mass flux in
the cloud is reduced. The details of the driving forces of
the outer shell are not fully understood yet, but the
observations provide the basis for some further speculations. One possibility for the driving force of the outer
flow is that the air adjacent to the inner shell could be
dragged along with the downdrafts inside the inner shell
through lateral turbulent transport of vertical momentum. Another idea is based on observations by Abma
et al. (2013), who showed that the minima of the buoyancy and of the vertical velocity fields in the buoyant
subsiding shell move toward the cloud interior with
different speed: the buoyancy minimum moves faster
toward the cloud interior compared with the velocity
minimum. However, neither explanation is easily reconciled with the observation that the outer shell is nearly
nonturbulent. Finally, one might also speculate that the
outer shell could be the very diluted remnants of a previous inner shell that is so diluted that the properties are
close to the environment and the turbulent kinetic energy has almost dissipated, but in which the air is still
subsiding because of inertia. The current measurements
do not necessarily favor any of these possible mechanisms, so further investigations of the outer shell are
needed. A starting point would be to perform similar
measurements but at different cloud heights.
AUGUST 2014
2821
KATZWINKEL ET AL.
We have presented measurements of the finescale
properties of cumulus cloud edges, obtained with the
helicopterborne measurement platform ACTOS. A statistical analysis of 217 clouds leads to a detailed picture of
the turbulent, thermodynamic, and microphysical structure of the subsiding-shell region including its changes
during cloud evolution from actively growing to decelerating and finally to dissolving. An analysis of conserved variables and the velocity and buoyancy fields
confirms that the subsiding shells are a result of mixing
between environmental and cloud air. The present observations indicate that clouds are influenced unequally
by the entrainment of environmental air depending on
their stage of development. This is caused by different
properties of the entrained air due to the increasing
thickness of the inner shell. Furthermore, these shells are
often characterized by higher turbulent energy dissipation rates than in the cloud. An initial effort toward
comparing measurements to the idealized development
of a cloud-edge mixing region in a direct numerical simulation gave some general agreement—most notably that
shell thickness increases monotonically as downdrafts
become more intense. The measurements further suggest
that the inner-shell region grows at the expense of the
cloud interior, as illustrated in Fig. 8. Many questions
remain, among which are the origin of entrained air
(lateral versus from cloud top) and the mechanism driving downward velocity in the observed outer shells.
Measurements under a wider range of environmental
conditions and at a larger range of heights as well as
computational studies bridging DNS and LES scales will
provide more insight. Finally, the influence of lateral
entrainment and subsiding shell formation on the evolution of cloud microphysical properties remains an open
problem.
Acknowledgments. We thank the two pilots Alwin
Vollmer and Milos Kapetanovic for the great helicopter
flights. Thanks also to Paul Archer and to National
Helicopters in Canada for organizing and providing the
helicopter service. Many thanks also to the team from
the Barbados Concorde Experience who hosted the
ACTOS and helicopter team. We are grateful to
Christoph Klaus and Dieter Schell from the enviscope
company for their excellent technical support during the
campaigns and acknowledge David Farrell and Damien
Prescod from CIMH for their support in terms of local
logistics. We gratefully acknowledge Deutsche Forschungsgemeinschaft (DFG) for funding this project
within the priority program Metstr€
om (SI 1534/2-2) and
the DFG-project (SI 1534/3-1). Raymond A. Shaw’s
participation in this work was supported by NSF Grant
AGS-1026123.
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